# Electric field drop exponentially

1. Jan 28, 2008

### ythaaa

Is there any situation where the electric field drop exponentially in free space? thanks

2. Jan 29, 2008

### mjsd

in free space? probably not...
but across a surface where total internal reflection occurs, some evanescent wave is transmitted, this wave is exponentially suppressed.

3. Jan 29, 2008

### Andy Resnick

For electromagnetism, any near field amplitude component decays exponentially with distance.

For electrostatics, I'm not sure. There may be a way to construct a set of charges such that the multipole expansion looks like the series expansion for an exponential function, but I have never seen one.

4. Jan 30, 2008

### Claude Bile

Evanescent (exponentially decaying fields) can be produced by;

- Total internal reflection.
- Guided modes in a waveguide.
- An EM diffracting off a sub-wavelength aperture or obstacle (Near-field).
- Exciting a charged surface at resonance (surface plasmons).

Claude.

5. Jan 30, 2008

### Ulysees

> For electrostatics, I'm not sure. There may be a way to construct a set of charges such that the multipole expansion looks like the series expansion for an exponential function

Or put a dielectric with spatially varying dielectric constant around a point charge in a homocentric manner. This would eliminate the inverse square and introduce the exponential. Here it is:

E = 1/4πε(r) Q / r^2

if ε(r) = a * exp(br) / r^2

then you've got a decaying exponential effect.

E = E0 * exp(-br)

Last edited: Jan 30, 2008
6. Jan 30, 2008

### jdavel

a field whose magnitude decays exponentially (either in 1-D or radially from some central point) has a non-zero divergence everywhere. so if by "free space" you mean no charge density, then I don't think such a field could exist anywhere in free space.

Last edited: Jan 30, 2008